Thanks mumslife, I've always thought x-DP (DD's dad) could have aspergers too, but he also has a vivid imagination and makes up great stories. I hope I didn't offend you by suggesting that people with aspergers/ASD can't have imagination - this is purely my own ignorance. 
Tough I am just starting to learn about this too!
She does sound similar to your DD Ineed. I don't know whether to try for a diagnosis or not. DD went to an excellent nursery which was also a specialist centre for children with special needs. Soon after she started they told me that they had some concerns and put her in what we called 'special measures'
- they had her doing small group work looking at following instructions and social interactions. They told me that they didn't think she had SEN, but that she was very strong willed and didn't seem to feel the need to comply or 'fit in' with other children. The phrase that really stuck with me was "if you've got a class of 30 children and ask them to do something; if 29 of them do it then you can almost guarantee that the 30th will too. DD won't; she'll just carry on doing what she wants to do." That sums her up, really - she's still just the same now.
She didn't really have special friends in YrR-2, just would play with whoever. As I said, this would often take the form of following boys around and goading them to chase her by pretending to be an animal; she does this thing where she hisses and grimaces and assumes a sort of attack stance. God I'm making her sound really odd aren't I.
She still does this, along with the assorted animal noises.
The thing is, she's very articulate and sounds much older and more confident than she is. She was a very late talker (if I'd realised at the time quite how delayed then I'd have sought help but I didn't know that many children her age). She had 2 or 3 words when I met my DP and she was 2yrs 3 months then. She wasn't really speaking in complete sentences at 3. Yet she started nursery at 3.8 and didn't stop talking from then on. Her infant school put her on the G&T list for 'linguistic intelligence' although her junior school didn't continue that. Her vocabulary amazes me sometimes and her use of words is really eccentric inventive. She sounds very mature but underneath it she's really not, bless her, and I think people expect more of her because she's so tall and loud and articulate. She just hasn't got the social skills and understanding to underpin it. 
The recent incident that brought it to the fore again was that my parents took her to a jubilee barn dance in their village. The children were all doing a barn dance where you had to have a partner. DD went around asking all the children (none of whom she knew) to dance with her. When they wouldn't, she refused to listen to my DM's explanation that you can only do it with a partner, went and stood in the middle and started dancing on her own. She didn't know the movements so she started sort of freestyling.
My Dparents didn't know whether to
or cringe for her! DM made my DstepF go and dance with her to stop the embarrassment, but DD refused to dance with him and got really angry!
She had no awareness at all of the inappropriateness of her behaviour.
When I talked to her on the phone the next day she told me that she didn't really like barn dancing because it's boring and 'I like to do my own thing Mummy' - this must be the most uttered phrase in our household. 
Sorry I've really wittered on.
I don't know whether there's anything to be gained from pursuing a diagnosis. It might help me understand her a bit better, maybe?